Enid, as a childminder I can say I would be delighted to take care of your two year old daughter!
I understand totally what you are saying, I went through the same experience with my daughter, she had no separation anxiety but just seemed overwhelmed by the sheer number of children , (only 24,) the size of the hall, children moving around constantly. She never cried but I knew that it wasn't for her or me. That's basically why I started to childmind - taking a few friends two year olds for a few afternoons or mornings to give them a break, and it became a regular committment.
I would also do activities with the children, as it is more fun with three and more worthwhile setting up the paint etc rather than one child. It is easy to give them individual attention but they also learn to share and take turns.
I have been studying the effect of "too much too soon. too early" for my degreein Early childhood studies, it is very revealing. I also explored nursery care in Switzerland when I was there, it doesn't exist as such!
Children go to playgroup, only 2/3 sessions up to 5 years of age, but it is family group ie mixed ages 0-6, day care with 8-10 chidren max. with two mothers, and a leader. (Varies fron Canton to Canton, this was Basle). They then go to kindergarten mornings only until they are 7/8 years old! The boy I used to nanny for is 8 in May and he is as school 8-12 only until September. Then he goes 8-12 and 2-4. home two hours for lunch! You get the message that children should be at home with their mothers as there is no provision for the lunchtime cover.
Do what is best for you and your daughter, I kept mine at home until they were both rising four and went to a kindergarten attached to a prep prep where they played everyday, a group of 10 children and they thrived on it.
My daughter still can remember her experience of playgroup even though she was only 2.5, but remebers kindergarten with great affection!
Good luck!
PS I tried to post this yesterday but the site was closed, but hope it helps